A particle of mass `m` is executing oscillations about origin on the x axis amplitude A its potential energy is given as`U(x) = beta x^(4)` where `beta` is constant x cooridirate of the particle where the potential energy is one third of the kinetic energy isA. `+- (A)/(2)`B. `+- (A)/(sqrt(2)`C. `+- (A)/(3)`D. `+- (A)/(sqrt(3)`

A particle of mass `m` is executing oscillations about origin on the x

1.	A particle of mass `m` is executing oscillations about origin on the x axis amplitude A its potential energy is given as`U(x) = beta x^(4)` where `beta` is constant x cooridirate of the particle where the potential energy is one third of the kinetic energy isA. `+- (A)/(2)`B. `+- (A)/(sqrt(2)`C. `+- (A)/(3)`D. `+- (A)/(sqrt(3)`
Answer» Correct Answer - B `U = beta x^(4)` (given) `:. U_(max) = beta .A^(4)` `k(x) = U_(max) - U(x) = betaA^(4) - betax^(4) = beta (A^(4) - x^(4))` `U(x) = (1)/(3)K(k)` (Given) `:.betax^(4) = (1)/(3) beta(A^(4) - x^(4))` `rArr 3 betax^(4) = beta A^(4) - betax^(4)` ` 4beta x^(4) = beta A^(4)rArr x^(4) =(A^(4))/(4)` `rArr x = +- (A)/(sqrt(2))`

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